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Using Stochastic Models in Risk and Capital Management in Life Assurance Tuesday 5 th April 2005 Craig Turnbull. Agenda. Introduction: Developments in the use of (internal) stochastic models in life assurance Why now? Who wants it? How does it work? What questions is it used to answer?
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Using Stochastic Models in Risk and Capital Management in Life Assurance Tuesday 5th April 2005 Craig Turnbull
Agenda • Introduction: Developments in the use of (internal) stochastic models in life assurance • Why now? Who wants it? • How does it work? • What questions is it used to answer? • Assessing Risk-Based Capital for With-Profits Business • Quantifying risks and their interaction • Using Models as a Capital Management Tool • Identifying and appraising candidate solutions • Questions and Answers
Introduction:Developments in the use of (internal) stochastic models in life assurance
What Developments? • Global life assurance industry developing large-scale internal stochastic asset-liability models • Sophisticated arbitrage-free multi-asset models • Complex liability models • Dynamic management rules, ‘000s model points, etc • Particularly in UK life industry and the top 20 multinational insurance groups
Why Now? • Regulatory compulsion (UK only) • Greater appreciation of risks in guarantees in life & pensions business • Less capital / risk appetite than 5 years ago • Appreciation that life / pensions ALM falling behind banking industry • Technology • Cheaper, faster
Who Wants It? • Regulators • FSA • Market-consistent guarantee costs (RBS / Pillar 1) • Risk-based capital assessment (ICA / Pillar 2) • Stochastic modelling approach required in US and Canada • Will other regulators follow FSA regime? • Accountants • IAS, FRS 27 (FRS 17) • European Embedded Value • Credit rating agencies • Risk-based capital adequacy • Calculation and communication • Internal management • Economic capital allocation and performance measurement • Risk / capital management • Product design / pricing
What can it deliver? • Quantification of costs, risks and capital requirements • Relative size of drivers • Risk dynamics • Diversification, interaction, non-linearity • Identification and appraisal of candidate management solutions • Informing trade-offs
Office - Specific Liability Features, Management Strategies Model Office Software Market-Consistent Balance Sheet / Capital Assessment / etc (Market – Consistent) Economic Scenario Generator Market Prices / Best-Estimates How Does it Work?
Approaches to measuring RBC • What approaches can be taken to assessing risk-based capital requirements for insurance liabilities? • Run-Off • Capital required to fund projected cashflow shortfalls with a specified level of confidence • Value-At-Risk • Capital required to fund a future market-consistent liability value with a specified level of confidence • Funding the cost of transferring market risk to market
With-Profit Implementation challenges • Run-Off • Estimating long-term asset return tails • Scarcity of relevant data • Projecting market-consistent balance sheet forward over multiple time horizons • Important if m-c balance sheet is a driver of decision rules
With-Profit Implementation challenges • VaR • Estimating 1-year asset return extreme tails • Conditional on recent market behaviour, option prices? • Nested simulations required (in theory!!) • Practical (approximate) implementation approaches
Individual Capital Assessment • Predominantly VaR-style definitions used currently • Capital required to produce 99.5% confidence that realistic liabilities are funded after one year • Given the above difficulties, how is VaR being implemented for With-Profits? • Unconditional asset modelling • Broadly two implementation approaches for VaR • Univariate • Multivariate
ICA for With-Profits – Univariate Approach • Calculate 99.5th percentile events for each risk factor, and obtain capital requirements for each risk factor • Calculate total capital requirement by applying a correlation matrix to the capital requirements for each risk factor • This assumes: • Risks are linear • Risks do not interact
ICA for With-ProfitsMultivariate Approach • Estimate sensitivities of realistic balance sheet to each risk factor • Use these to project RBS to end-year (using stochastic asset model) • Read off 99.5th percentile discounted loss
Illustrative Example • Liability is a 10-yr equity total return put option with strike at-the-spot • Interest rate of 5% • Volatility of 20% • Nominal of £1,644m • Current market value of put option of £100m • Assume assets backing guarantee cost are invested in equities • And any assets required in excess of guarantee cost are invested in cash
RBC under Univariate approach:Risk Contributions • 99.5th percentile equity return is -36% • Liability increases from 100 to 235 • Assets fall from 100 to 64 • Equity capital requirement is 163 • [(235-100) – (100-64)]/ 1.05 • 99.5th percentile rise in option-implied equity vol is 5% • Liabilities increase from 100 to 160 • Assets do not change in value • Vol capital requirement is 57 • 99.5th percentile interest rate fall is 1.5% • Liabilities increase from 100 to 157 • Assets do not change in value • Interest rate capital requirement is 54
RBC under Univariate approach:Allowing for diversification • Sum of capital requirements is £274m • But this assumes perfect correlation • Assume correlations of: • -0.3 between equities / interest rates • -0.4 between equities / option-implied vol • +0.1 between interest rates / implied vol • Implies capital requirement of £185m • Diversification benefit of 32%
RBC under Multivariate approach • Use a number of sensitivity tests: • 20% equity fall increases liabilities from 100 to 159 • 40% equity fall increases liabilities from 100 to 259 • 0.85% interest rate fall increases liabilities from 100 to 130 • 2% option-implied interest rate rise increases liabilities from 100 to 124 • Could use many more, e.g. 20% equity fall after 1% interest rate fall, etc… • Use ‘greeks’ to project liabilities in each 1-yr asset simulation
Asset / Liability Projection as a function of equity returns
RBC: Concluding Thoughts • Current implementations of the multivariate approach produce similar capital requirements to univariate approach • In example, capital requirements were £187m and £185m • But mulitvariate approach is inherently more flexible and transparent • Sophistication can be developed incrementally • More useful as a risk management tool (identifying and appraising candidate management solutions)
Correlations: An Aside • Most life offices are exposed to falls in equities and falls in interest rates • (Also true for Defined Benefit pension funds) • Negative correlation assumption between equities and interest rates implies ‘natural hedge’ • i.e. Big diversification benefit • What if we reduce equity / interest rate correlation?
Appraising hedging solutionsEstimating economic capital Neutralising equity exposure: reductions in ICA and RCM Option strategy improves gamma and vega matches: significant reduction in ICA, no impact on RCM
Monitoring and managing a hedging strategy • Liability risk exposures will change over time as financial markets move • Any hedge is unlikely to be static for long periods. The extent to which this is the case will depend on choice of hedging solution – e.g. how well matched is equity gamma? • Hedging performance can be regularly monitored (e.g. quarterly) and, when appropriate, re-balanced. Impact of Interest Rate and Equity Market Interaction on Realistic Guarantee Cost e.g. cash guarantee’s equity delta can double when the yield curve falls by 100bp.
Concluding Thoughts • Changes in regulatory / accounting / rating agency regimes mean significant step towards convergence in various capital / value / profit measures • Reduces constraints to managing economic risks • New valuation tools allow capital market solutions to be more effective at mitigating market risks in life assurance business
